Potentially Broken Strategy

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MasN
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Joined: 26 December 2015, 23:45

Potentially Broken Strategy

Postby MasN » 20 August 2017, 22:48

So I believe this strategy is "against the spirit of the game".

The strategy works on any difficulty, but requires at least 4 players. In addition, the 4 players have handicapped themselves: If a normal Hanabi player says "I give Bob a 4 clue. These cards are 4s", all the handicapped player says is "I give Bob a 4 clue"

I believe this strategy is the best possible strategy, and gives the maximum possible score for any deck configuration.

The idea is in a 4 player game, there are 30 possible clues to give, and we can assign each one a number from 0 to 29. There are also only 30 possible cards, and we can also assign each one a number from 0 to 29.

Whenever a player gives a clue, instead of doing it normally, they add the numbers of his teammates rightmost unclued fireworks, take it modulo 30, then give the corresponding clue. Mark each of these fireworks added this way as "clued". Each person can reverse the process to find out the exact identity of each of their fireworks.

From this algorithm, you can make a strategy that wins the game, because its as if every card was drawn face up.

If there is any problem with this strategy, please tell me. If not, one way to stop it is require that each clue hits at least 1 card.

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RicardoRix
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Re: Potentially Broken Strategy

Postby RicardoRix » 21 August 2017, 16:30

this sounds like it would work while you have clues, but then you would run out of clues..
IIRC you don't get a clue back if you play a correct card, only when you discard a card.

Have you tried this strategy out yourself?

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MasN
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Re: Potentially Broken Strategy

Postby MasN » 21 August 2017, 20:48

Haven't tried it myself yet. Though each clue identifies 3 cards, and you can make it so that every discard is a safe discard.

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RicardoRix
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Re: Potentially Broken Strategy

Postby RicardoRix » 21 August 2017, 22:27

So you've got 10 different clues and 3 other players, so that does give you 30 combinations.
If there are 30 different cards, how are you managing to signal 3 different cards with 1 clue?
looks like 1 clue for 1 card to me....

E.G. Red is 1-5, Yellow 6-10, Green 11-15, Blue 16-20, White is 21-25.

Lets say I have 1B, 2B, 2W
16 + 17 + 22 = 55.
55 % 30 = 25.

How is that different to say 1B, 4R, 5R
16 + 4 + 5 = 25.

and even if you could, which order are the cards in, or rather in your version - which card belongs to which player...?

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MasN
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Re: Potentially Broken Strategy

Postby MasN » 22 August 2017, 02:43

You can only signal 1 card per player with this strategy, but you can signal a card for each player. Simply add up the numbers on their cards and take it modulo 30. Since each player can see the other cards you signalled, they can subtract those numbers and derive their own.

The players can simply agree that each card signalled is the right most card of each player not already signalled in this fashion.

So say I have 14, 18, and 23
Player B has 29, 5, and 16
Player C has 7, 17, and 15
Player D has 13, 25, and 4

I'd signal the 16, the 15 and the 4 by adding them yp to get 35, and then taking it modulo 30 to get 5.
Now player B knows that ?+15+4 (mod 30) is 35, and thus he has a 16.

Then, player B clues my 23, as well as the 17 and 25, as these are the rightmost unclued cards.

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RicardoRix
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Re: Potentially Broken Strategy

Postby RicardoRix » 22 August 2017, 09:26

oh yes, wow!

That is incredibly clever!

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RicardoRix
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Re: Potentially Broken Strategy

Postby RicardoRix » 23 August 2017, 11:33

Actually that reminds me.

Is the actual answer 42?

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nandblock
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Re: Potentially Broken Strategy

Postby nandblock » 23 August 2017, 18:06

I can see how this can clue cards but it is only half a strategy. Given the limits on clues and the fact that playing cards except 5s doesn't give you clues, how would this approach work in practice?

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MasN
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Re: Potentially Broken Strategy

Postby MasN » 27 August 2017, 16:01

Like the normal game, you can still discard duplicate cards. The discards should give you enough clues to clue every card that is drawn when we are talking about a 1 clue : 3 cards ratio.

florrat
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Joined: 12 March 2016, 03:27

Re: Potentially Broken Strategy

Postby florrat » 01 November 2017, 04:39

I implemented a strategy as a Python script similar to this idea. The main difference in strategy is that instead of telling each player about one of their cards, the strategy tells each other player what to do. I like this idea too, though. I'm not sure which is more efficient. I'm afraid that with this strategy you run out of clues quite quickly with 4 players, though.

I wrote up a detailed description of my strategy here:
https://github.com/fpvandoorn/hanabi/bl ... _player.md
My strategy only uses 9 possible clues and also no player looks to which cards the cluer actually points when cluing.

It wins (achieves maximal score) about 80% of the games (note that even if you can look at all cards, you still lose about 2-3% of the games - and about 11% of the games with 2 players). The main improvement it could make would be endgame reasoning, but that is tricky to implement.


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